Finite Group Databasebeta

← C₄×C₄₇×C₄₉ #22604237

Subgroups — C₄×C₄₇×C₄₉ #22604237

Order 9212.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₄₇×C₄₉	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₇×C₄₇	C₇	1	1	yes	maximal, characteristic
4	C₂×C₇×C₄₇	C₂×C₇	1	1	yes	characteristic
5	C₇×C₄₇	C₄×C₇	1	1	yes	characteristic
6	C₄×C₄₉	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₄×C₄₇	C₄₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₄₉	C₂×C₄₇	1	1	yes	characteristic
9	C₂×C₄₇	C₂×C₄₉	1	1	yes	characteristic
10	C₄₉	C₄×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₄₇	C₄×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₄×C₇	C₇×C₄₇	1	1	yes	characteristic
13	C₂×C₇	C₂×C₇×C₄₇	1	1	yes	characteristic
14	C₇	C₄×C₇×C₄₇	1	1	yes	characteristic
15	C₄	C₄₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₄₇×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂×C₇	C₂×C₇×C₄₇
socle	C₂×C₇×C₄₇	C₂×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₄₇×C₄₉	C₄	direct (N × H)
6. C₄×C₄₉	C₄₇	direct (N × H)
7. C₄×C₄₇	C₄₉	direct (N × H)
10. C₄₉	C₄×C₄₇	direct (N × H)
11. C₄₇	C₄×C₄₉	direct (N × H)
15. C₄	C₄₇×C₄₉	direct (N × H)